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Topic: Matheology § 224
Replies: 84   Last Post: Apr 20, 2013 4:43 PM

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Jesse F. Hughes

Posts: 9,776
Registered: 12/6/04
Re: Matheology S 224
Posted: Apr 14, 2013 11:29 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Nam Nguyen <namducnguyen@shaw.ca> writes:

> On 14/04/2013 7:40 PM, Jesse F. Hughes wrote:
>> Nam Nguyen <namducnguyen@shaw.ca> writes:
>>

>>> On 14/04/2013 4:58 PM, Nam Nguyen wrote:
>>>> On 14/04/2013 4:28 PM, Nam Nguyen wrote:
>>>>> On 14/04/2013 3:41 PM, fom wrote:
>>>>>> On 4/14/2013 3:40 PM, Nam Nguyen wrote:
>>>>>>> On 14/04/2013 9:19 AM, Nam Nguyen wrote:
>>>>>>>> On 14/04/2013 12:44 AM, Nam Nguyen wrote:
>>>>>>>>>
>>>>>>>>> Can you or they give me a straightforward statement of understanding
>>>>>>>>> or not understanding of Def-1, Def-2, F, F' I've requested?

>>>
>>>> Also, if you'd like to help the debate about my cGC thesis,
>>>> why don't you offer a closure on my Def-1 and Def-2.
>>>>
>>>> I'm serious in saying that it's crucial to my thesis about
>>>> cGC. If such a simple definition of set-membership truth-relativity
>>>> is technically wrong, inconsistent, or what have you, of course my
>>>> entire thesis would falter to pieces. And you will never hear me attempt
>>>> on the relativity of cGC truth anymore.
>>>>
>>>> But I do need a closure on these 2 definitions.

>>>
>>> Naturally _everyone_ who could constructively contribute to the closure
>>> would be welcomed. And if I miss anyone in the below list I'd like
>>> to apologize in advance.
>>>
>>> In particular, with some reasons no so important of my own, I'd
>>> like appreciate in advance if Chris Menzel, Herman Rubin, Franz
>>> Fritsche, Aatu Koskensilta, George Greene, Dave Seaman, Rupert,
>>> Jim Burns, could offer some analysis and closure on my Def-1 and Def-2
>>> as presented in:
>>>
>>> http://groups.google.com/group/sci.math/msg/e6f47fad548fbb97?hl=en

>>
>> You sure seem eager for some comments. I know I'm not on the list,
>> but I'll bite.

>
> First is my non-technical caveat about the list of names. It obviously
> can only be a finite list so any in which way I would have listed,
> an apparent "offending" would occur however unintentionally. And I
> did apologize in advance for that. To prove the point, after I sent
> out the list I realized I forgot to mention Mike Oliver. The reason
> for the finite list, as I've said is of _my own reason but isn't an_
> _important one_ .
>
> Based on some dialogs in the past, I believe correctly or incorrectly
> those I mentioned _might_ be aware of some of the technical motivation
> behind my presenting for years. That's all: just the motivation; I
> certainly did _not_ chose the list based on who I'd think be "on my
> side", so to speak.
>
> In any rate, I did invite "_everyone_ who could constructively
> contribute ...".
>

>>
>> ,----
>> | Given a set S:
>> |
>> | Def-1 - If an individual (element) x is defined to be in S in a finite
>> | manner or inductively, then x being in S is defined an absolute
>> | truth.
>> |
>> | Def-2 - If an individual (element) x isn't defined to be in S in a
>> | finite manner or inductively, then then x being in S, or not,
>> | is defined as a relative truth, or falsehood, respectively
>> |
>> | Would you et al. understand Def-1 and Def-2 definitions now?
>> `----
>>
>> I don't understand the definitions at all, because I don't know what
>> it means that "x is defined to be in S in a finite manner or
>> inductively."

>
> Let's do the finite case first, and I will address the "inductively"
> case after.
>
> The finite case is the quite similar to the definition of FOL
> syntactical theorems, where a proof of a formula is a _finite_
> _sequence of proof-steps_ conforming to a certain patterns (of
> application of rules of inference). We have no choice but take
> for granted what certain priori, "finite", "sequence", "steps",
> etc... would mean.
>
> What Def-1 says in the finite case is that given a set S, if an
> element x is proven, verified to be in a non-empty _finite subset_
> of S then x being a member of S is defined to be an absolute truth.
> Naturally here we also take for granted what it'd mean by "finite
> subset", an element being in a set or not, to know or to verify an
> element to be or not to be in a finite set, etc...


It seems to me that we are mixing syntactic and semantic notions here.

Do you mean: let t and s be any terms of the language of ZF (or
whatever) and suppose that

ZF |- (E x)(x c s & x != {} & x is finite & t in x)

then "t in s" is an absolute truth.

>> In fact, I understand almost none of that phrase. I don't know what
>> it means for x to be "defined to be in S", much less so defined "in a
>> finite manner or inductively".

>
> I'm not sure I understand your objection here: isn't defining a set S
> is defining certain elements x's _to be in S_ ?


That's certainly not how I would put it. Is there any difference
between the following two statements?

x is defined to be in S.

x is in S.

>> So, there you have it -- a response
>
> Sure. Likewise I think I've explained your concern, in the finite case.
>
> Are you with me so far?


Not particularly, but we'll see how it goes.

--
Jesse F. Hughes
"It is not as satisfying to disagree with a book."
-- Russell Easterly, on why he argues against set theory without
reading a book on set theory.


Date Subject Author
4/12/13
Read Re: Matheology § 224
Alan Smaill
4/12/13
Read Re: Matheology § 224
namducnguyen
4/12/13
Read Re: Matheology § 224
Frederick Williams
4/12/13
Read Re: Matheology § 224
fom
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
fom
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
fom
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology S 224
Jesse F. Hughes
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
Peter Percival
4/14/13
Read Re: Matheology S 224
fom
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
fom
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
fom
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
Jesse F. Hughes
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
Jesse F. Hughes
4/14/13
Read Re: Matheology S 224
namducnguyen
4/16/13
Read Re: Matheology S 224
namducnguyen
4/16/13
Read Re: Matheology S 224
namducnguyen
4/16/13
Read Re: Matheology S 224
Jesse F. Hughes
4/16/13
Read Re: Matheology S 224
namducnguyen
4/16/13
Read Re: Matheology S 224
fom
4/17/13
Read Re: Matheology S 224
namducnguyen
4/17/13
Read Re: Matheology S 224
fom
4/17/13
Read Re: Matheology S 224
namducnguyen
4/17/13
Read Re: Matheology S 224
Jesse F. Hughes
4/17/13
Read Re: Matheology S 224
Jesse F. Hughes
4/17/13
Read Re: Matheology S 224
namducnguyen
4/20/13
Read Re: Matheology S 224
namducnguyen
4/17/13
Read Re: Matheology S 224
Frederick Williams
4/17/13
Read Re: Matheology S 224
Frederick Williams
4/17/13
Read Re: Matheology S 224
fom
4/17/13
Read Re: Matheology S 224
Frederick Williams
4/17/13
Read Re: Matheology S 224
fom
4/17/13
Read Re: Matheology S 224
fom
4/18/13
Read Re: Matheology S 224
namducnguyen
4/18/13
Read Re: Matheology S 224
Frederick Williams
4/18/13
Read Re: Matheology S 224
namducnguyen
4/19/13
Read Re: Matheology S 224
Frederick Williams
4/19/13
Read Re: Matheology S 224
namducnguyen
4/20/13
Read Re: Matheology S 224
Frederick Williams
4/19/13
Read Re: Matheology S 224
Frederick Williams
4/19/13
Read Re: Matheology S 224
namducnguyen
4/20/13
Read Re: Matheology S 224
Frederick Williams
4/14/13
Read Re: Matheology S 224
Jesse F. Hughes
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
Jesse F. Hughes
4/14/13
Read Re: Matheology S 224
namducnguyen
4/14/13
Read Re: Matheology S 224
Peter Percival
4/15/13
Read Re: Matheology § 224
Peter Percival
4/14/13
Read Re: Matheology § 224
namducnguyen
4/14/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
Frederick Williams
4/13/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
namducnguyen
4/15/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
fom
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
Frederick Williams
4/14/13
Read Re: Matheology § 224
Frederick Williams
4/14/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
Peter Percival
4/13/13
Read Re: Matheology § 224
namducnguyen
4/13/13
Read Re: Matheology § 224
namducnguyen

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